Confidence intervals worksheet with answers

Free printable Confidence intervals worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
n = 40, σ = 14LU = ?x̄ = 132.5E99%

A sample of 40 measurements has mean 132.5. The population standard deviation is known to be 14. Find the upper limit of the 99% confidence interval for the mean.

n = 40x̄ = 132.5σ = 1499%
upper limit =
2.Easy
192.3x̄205.799%

A 99% confidence interval for a mean, computed from 100 observations with a known population standard deviation, is [192.3, 205.7]. What standard deviation σ was used?

[192.3, 205.7]n = 10099%
σ =
3.Medium
μ₁ − μ₂0LU = ?x̄₁ − x̄₂E95%

The battery life of two phone models is compared. Model 1: 80 phones, mean 95 h, known standard deviation 17 h. Model 2: 40 phones, mean 100.5 h, known standard deviation 3 h. Find the upper limit of the 95% confidence interval for μ₁ − μ₂.

n₁ = 80x̄₁ = 95 hσ₁ = 17 hn₂ = 40x̄₂ = 100.5 hσ₂ = 3 h95%
upper limit = h
4.Medium
n = 30, s = 16.5LUx̄ = 85.5E = ?90%

A sample of 30 items has mean 85.5 and standard deviation s = 16.5. The population is roughly normal. Find the margin of error E of a 90% confidence interval for the mean.

n = 30x̄ = 85.5s = 16.590%t(29) = 1.699
E =
5.Hard
σ = 13, n = ?x̄ − Ex̄ + Ex̄E = 2.590%

The population standard deviation is 13. How large a sample n do you need so that a 90% confidence interval for the mean has a margin of error of at most 2.5?

σ = 13E = 2.590%
n =
6.Hard
n = 20σ = ?Us = 5.695%

The diameters of 20 machined shafts have a sample standard deviation of 5.6 µm. Assuming the diameters are normally distributed, find the lower limit σ of the 95% confidence interval for the population standard deviation. With df = 19, 2.5% of the χ² distribution lies below 8.907 and 2.5% lies above 32.852.

n = 20s = 5.6 µmχ² = 8.907, 32.852
σ = µm

Answer key

  1. 1. upper limit = 138.2
  2. 2. σ = 26.01
  3. 3. upper limit = −1.66 h
  4. 4. E = 5.118
  5. 5. n = 74
  6. 6. σ = 4.259 µm

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